Homogeneous Studies of Transiting Extrasolar Planets. II. Physical Properties
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Mon. Not. R. Astron. Soc. 000, 000–000 (0000) Printed 2 January 2009 (MN LATEX style file v2.2) Homogeneous studies of transiting extrasolar planets. II. Physical properties John Southworth? Department of Physics, University of Warwick, Coventry, CV4 7AL, UK 2 January 2009 ABSTRACT I present an homogeneous determination of the physical properties of fourteen transiting ex- trasolar planetary systems for which good photometric and spectroscopic data are available. The input quantities for each system are the results of the light curve analyses presented in Paper I, and published measurements of the stellar velocity amplitude, effective temperature and metal abundance. The physical properties are determined by interpolating within tabu- lated predictions from stellar theory to find the optimal match to these input data. Statistical uncertainties are found using a perturbation algorithm, which gives a detailed error budget for every output quantity. Systematic uncertainties are assessed for each quantity by comparing the values found using several independent sets of stellar models. As a theory-free alternative, physical properties are also calculated using an empirical mass–radius relation constructed from high-precision studies of low-mass eclipsing binary stars. I find that the properties of the planets depend mostly on parameters measured from the light and radial velocity curves, and have a relatively minor sensitivity to theoretical predictions. In contrast, the orbital semimajor axes and stellar masses have a strong dependence on theoretical predictions, and their systematic uncertainties can be substantially larger than the statistical ones. Using the empirical mass–radius relation instead, the semimajor axes and stellar masses are smaller by up to 15%. Thus our understanding of extrasolar planets is currently limited by our lack of understanding of low-mass stars. Using the properties of all known transiting extrasolar planets, I find that correlations between their orbital periods, masses and surface gravities are significant at the 2–3 s level. However, the separation of the known planets into two classes according to their Safronov number is weaker than previously found, and may not be statistically significant. Three systems, HAT-P- 2, WASP-14 and XO-3, form their own little group of outliers, with eccentric orbits, massive planets, and stars with masses ∼1.3M¯. The detailed error budgets calculated for each system show where further observations are needed. XO-1 and WASP-1 could do with new transit light curves. TrES-2 and WASP-2 would benefit from more precise stellar temperature and abundance measurements. Veloc- ity measurements of the parent stars are vital for determining the planetary masses: TrES-1, XO-1, WASP-1, WASP-2 and the OGLEs need additional data. The homogeneous analysis presented here is a step towards large-scale statistical studies of transiting extrasolar planetary systems, in preparation for the expected deluge of new detections from CoRoT and Kepler. Key words: stars: planetary systems — stars: binaries: eclipsing — stars: binaries: spectro- scopic 1 INTRODUCTION 300 extrasolar planets at the time of writing1. The shortcoming of this technique is that it does not allow us to obtain a detailed under- The discovery of extrasolar planets, made possible through high- standing of individual objects. For each system it is typically pos- precision radial velocity observations of dozens of stars (Mayor & sible to obtain only the orbital period and eccentricity, and lower Queloz 1995), is one of the great scientific achievements of the limits on the mass and orbital separation of the planet. twentieth century. Radial velocity surveys have have been remark- The detection of the first transiting extrasolar planetary sys- ably successful so far (Udry & Santos 2007), discovering nearly ? E-mail: [email protected] 1 See http://exoplanet.eu/ for a list of known extrasolar planets. °c 0000 RAS 2 John Southworth tem, HD 209458 (Charbonneau et al. 2000; Henry et al. 2000), has crepancy arises from undetectable systematic errors or starspots by demonstrated the solution to this problem. By modelling the light obtaining several independent light curves, each covering the same curve of a transiting extrasolar planetary system (TEP), adding in transit event of a TEP. radial velocity measurements of the star, and adopting one addi- In this work I describe and perform the second stage of the tional constraint from elsewhere, it is possible to determine the analysis: derivation of the physical properties of the fourteen TEPs masses and radii of both the star and planet. This information al- studied in Paper I. This uses the results of the light curve analy- lows the study of the chemical compositions of the two compo- ses, radial velocity measurements, and additional constraints from nents, and thus the formation and evolution of stellar and planetary theoretical stellar model predictions. Several different sets of stel- systems. lar models are used, allowing the systematic error inherent in this Approximately fifty TEPs are currently known, the major- method to be assessed for every output quantity. I also calculate ity discovered through wide-field photometric variability surveys. detailed error budgets for each TEP, showing what further observa- Some estimates of the masses and radii of the components are avail- tions will be useful for each system. As a theory-free alternative to able for each system, but these have been determined in a variety stellar model calculations, I also consider an empirical mass–radius of ways and using a wide range of additional constraints besides relation obtained from high-accuracy studies of 0.2–1.6M¯ eclips- photometric and radial velocity measurements. We are now at the ing binary star systems. The constraints are discussed in Section 2, threshold of statistical studies of the properties of TEPs, for which and applied to each TEP in Section 3. This leads to an homoge- homogeneous analyses are a fundamental requirement. This work neous set of physical properties for the fourteen TEPs (Section 4). is the second instalment of a series of papers intended to provide an Finally, the properties of all known TEPs are compiled and studied homogeneous study of the known TEPs. A recent paper by Torres, in Section 5. Winn, & Holman (2008, hereafter TWH08) has the same goal but differences in the method of analysis, particularly concerning the light curve modelling process. Each individual TEP is here studied in a two-stage process, the first stage being detailed modelling of all available good light 2 METHOD OF ANALYSIS curves of the system, and the second stage being the inclusion of The modelling of a set of light curves of a TEP gives four quanti- 3 additional observational and theoretical information to derive the ties which are important here (Paper I): the orbital period (Porb), physical properties of both star and planet. Whilst the first stage has the inclination of the orbit with respect to the observer (i), and the little or no dependence on theoretical calculations, the second stage, fractional radii of the star and planet, which are defined to be presented here, is reliant on the predictions of stellar evolutionary models. RA Rb rA = rb = (1) In Paper I (Southworth 2008) I tackled stage one: a detailed a a analysis of the light curves of the fourteen TEPs for which good where RA and Rb are the (absolute) stellar and planetary radii and a light curves were then available. The modelling process was per- is the orbital semimajor axis. To first order, there are four quantities 2 formed using the JKTEBOP code (Southworth et al. 2004a,b), that are directly measurable from a transit light curve (separation which represents the components of an eclipsing binary system in time, depth, overall duration and duration of totality) and four using biaxial spheroids (Nelson & Davis 1972; Popper & Etzel derived quantities (Porb, i, rA and rb), so these derived quantities 1981). Random errors were assessed using Monte Carlo simula- are well determined when the available data give the shape of the tions (Southworth et al. 2004c, 2005b) and systematic errors us- transit reliably. The light curve alone does not (apart from Porb) ing a residual-permutation algorithm (Jenkins et al. 2002). Careful have any direct dependence on the absolute scale of the system. thought was give to the treatment of limb darkening: five differ- Note that i is well constrained by a single good light curve, contrary ent limb darkening laws were tried (see Southworth et al. 2007a) to some statements in the literature (see Paper I). and the coefficients of the laws were empirically determined where As well as Porb, i, rA and rb, it is possible to measure the or- possible. Theoretically predicted limb darkening coefficients were bital velocity amplitude of the star, KA, from radial velocity mea- found to be in harmony with those obtained for most TEPs, but surements. However, one additional quantity or constraint is needed were clearly unable to match the results of the highest-quality data to be able to calculate the physical properties of the system. This (Hubble Space Telescope observations of HD 209458). constraint is normally derived from stellar evolution theory, but The results found in Paper I were generally in good agreement in some cases an accurate Hipparcos parallax or angular diame- with published studies, but for both HD 189733 and HD 209458 ter is available which allows stellar theory to be circumvented (e.g. the analysis